Linear recurring sequence subrgroups in finite fields

Owen J. Brison, J. Eurico Nogueira

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

Given a finite field F and a linear recurrence relation over F it is possible to find, in a fairly "obvious" way, a finite extension L of F and a subgroup M of the multiplicative group of L such that the elements of M may be written, without repetition, so as to form a cyclically closed sequence which obeys the recurrence. Here we investigate this phenomenon for second-order recurrences; the situation in which F has prime order and the characteristic polynomial of the relation is irreducible over F is described.

Original languageEnglish
Pages (from-to)413-422
Number of pages10
JournalFinite Fields And Their Applications
Volume9
Issue number4
DOIs
Publication statusPublished - 1 Jan 2003

Keywords

  • Finite field
  • Group permutation polynomial
  • Linear recurrence relation
  • Subgroup

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